ABC Lattices @Home

ABC Lattices @HOME is a research project that uses Internet-connected computers for searching for good abc-triples. Unlike ABC@Home, this project is not aiming for a thorough search of a certain range of numbers. Instead, we are trying to find good triples with the help of a specialized algorithm and educated guesses in areas beyond 2^100. You can participate by downloading and running a free program on your computer.

The application ABC Eval runs an algorithm which aims to find good abc-triples.

abc-triples are three integers (a, b and c) which satisfies the following conditions: a + b = c (now that looks easy, right?) The greatest common divisor of a and b is 1 (that's the tricky part) But it's getting trickier: Ask me what good abc-triples are!

First, you need to know, that the radical, rad(x), of a number is the product of distinct prime numbers of x.

Then, the quality of an abc-triple is defined as q(abc) = log( c ) / rad( a*b*c )

A good abc-triple has a quality greater than 1.4

It's part of my masters thesis to evaluate an algorithm for finding good abc-triples. Good abc-triples are very rare, yet it's unknown if there are infinitely many of them. Studying the nature of abc-triples and their distribution helps solving this so-called abc-conjecture.

Great! The Websites of the mathematical faculity of the University of Leiden are a great point to start.

The goal of ABC@home is a thorough and complete list of every abc-triple within certain bounds. At the moment, their list goes roughly up to triples with c less than 2^63. Other searches already found many good triples within c < 10^30. ABC lattices @ Home strives to find as many good abc-triples as efficient as possible, outside of anybody elses numerical ranges (as we know them). We are not affiliated with ABC@home in any way, but we share the same passion for the topic.

ABC Lattices @HOME is based at Hochschule RheinMain - University of Applied Sciences It is as part of my (Jan Gampe) masters thesis 'Parallel algorithms and the abc-conjecture'

• Website: http://boinc2.cs.hs-rm.de/abclll/
• Join to team: Ukraine

• First seen on: 29 Apr 2013
• Date of completion: <font color="orange"><strong>Project's Under Construction</strong></font>

The applications provided are designed for Pentium 3 machines or better, and have been tested under the following OS'ses:

• GNU/Linux 2.6 or newer (32/64 bit)
• Windows XP, Vista, 7 (8 is untested yet)
• OS X (any 64bit Apple machine should handle it)